Mesoscopic methods

Since MPC dynamics yields the hydrodynamic equations on long distance and time scales, it provides a mesoscopic simulation algorithm for investigation of fluid flow that complements other mesoscopic methods. Since it is a particle-based scheme it incorporates fluctuations, which are essential in many applications. For macroscopic fluid flow averaging is required to obtain the deterministic flow fields. In spite of the additional averaging that is required the method has the advantage that it is numerically stable, does not suffer from lattice artifacts in the structure of the Navier-Stokes equations, and boundary conditions are easily implemented. 

Of course, the macroscopic equations cannot actually be derived from the microscopic ones. In practice they are pieced together from general principles and experience. The stochastic mesoscopic description must be obtained in the same way. This semi-phenomenological approach is remarkably successful in the range where the macroscopic equations are linear, see chapter VIII. In the nonlinear case, however, difficulties appear, which can only be resolved by the improved, but still mesoscopic, method of chapter X. 

Table 6.2 summarizes the mesoscopic methods that have been successfully applied to study hydrate properties. These are categorized as methods that provide a spatial resolution on the order of microns. 

Mesoscopic Methods IR microscopy (16, 17) Single crystal membrane (14, 15) Single crystal membrane/tracer... 

In recent years, there has been great interest in developing physically inspired computational models based on the idea that the dynamics of the motion of fluid and interfaces can be represented in terms of the collective behavior of interactions of quasi-particle populations at scales smaller than macroscopic, but larger than molecular scales. These models fall in the class of mesoscopic methods - the LBM [6, 42, 45] being one. The LBM is generally based on minimal discrete kinetic models whose emergent behavior, under appropriate constraints, corresponds to the... 

Coarse-grained particle methods Huid particle model Mesoscopic method... 

Mesoscopic methods include several field-based approaches such as cell dynamical systems (CDS), mesoscale density functional theory (DFT), and self-consistent field (SCF)" theory. Most of these methods are related to the time-dependent Ginzburg-Landau equation (TDGL) ... 

A problem area that is not so amenable to mesoscale methods is polymer crystallization. This has proven to be one of the most difficult computational challenges in all of polymer science because the pertinent phenomena operate simultaneously over a wide range of length scales. The pol5uner crystallizes into a particular space group because of atomic detail, and the mechanical properties of the crystallites are determined by, and can only be calculated reliably with, atomic force fields with all atoms represented (126,127). Yet the size of the crystallites or spherulites is so large as to require mesoscopic methods for comprehension. But a crystalline polymer is almost never 100% crystalline. The interphases between crystalline and amorphous domains, with the possibilities for adjacent or nonadjacent reentry and tie-chain distributions, are critical to the properties of semicrystalline polymers. Only recently have models been developed (203) to rigorously address this problem area. 

Mesoscopic method Fluid particle model Coarse-grained particle methods... 

Mesoscopic Methods p Single crystal Pameation (Single crystal scale)-] FTIR Interference Microscopy... 

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